David Cameron has been accused of inconsistency and "shooting from the hip" by some Conservative MPs who criticised his decision to remain silent over Gary Barlow's tax affairs after lambasting Jimmy Carr.

As Downing Street said the prime minister had been too busy to fulfil his pledge to look at Barlow's tax affairs, senior Tories were privately warning that the prime minister risked looking foolish.

"This is so typical of our prime minister. This is all about shooting from the hip without thinking through the consequences. He looks rather foolish. Downing Street seems incapable of any long-term thinking," one said.

Conservative MPs accused the prime minister of adopting an inconsistent approach after he singled out Carr for criticism while refusing to be drawn on Barlow. The two entertainers were named by the Times [£] this week in an investigation into celebrities who have taken part in tax avoidance schemes.

Carr, who tweeted on Thursday that he had made a "terrible error of judgment", sheltered £3.3m in the Jersey-based K2 scheme, which dramatically reduced his tax liability by lending him back money. The Times reported on Wednesday that some members of Take That, including Barlow, invested at least £26m in a tax avoidance scheme. Both schemes are legal.

In an interview with ITV News at the G20 summit in Mexico, Cameron was highly critical of Carr. But he was less forthcoming about Barlow, a Conservative supporter who appeared alongside him during the 2010 election.

"I will have a look at that scheme," the prime minister said on ITV News on Wednesday of Take That's tax arrangements. "I got up this morning and I managed to read about this Jimmy Carr situation and this K2 idea – the idea of putting money in an offshore account and getting a loan back. That seems to me just straightforward tax avoidance but the Treasury will have to look into it. But the Gary Barlow situation? As soon I get in front of a computer I will have a look at it."

Downing Street said the prime minister had still not had time to read the Times report about Barlow. "He has been very busy," the No 10 spokeswoman said of Cameron, who hosted Aung San Suu Kyi over lunch at Chequers on Friday.

No 10 drew a distinction on Thursday between tax avoidance and "aggressive" tax avoidance. By Friday it simply said it would not be providing a "running commentary" on individual tax affairs.

Lord Oakeshott of Seagrove Bay, the former Lib Dem Treasury spokesman, said: "I think on Jimmy Carr, [Cameron's] problem is he didn't give £50 to the Tories. Then Cameron wouldn't have objected to it. The serious point is there is a difference between morally repugnant and illegal, and I think it is right to draw that distinction, but the key point for David Cameron as the prime minister and George Osborne – who said it was morally repugnant – is what are we actually going to do about it now?

"How are we going to make this behaviour that is morally repugnant legally repugnant as well? A lot of this activity is deeply damaging to the country – we need the money – and it's also deeply unfair. It is not technically illegal because the advisers to these people are far better organised than HMRC."